Properties of Integers Worksheet

1. When the prime numberkis multiplied by 2, the result is 1 less than another prime number. Which of the following is NOT a possible value ofk?(a) 2(b) 3(c) 5(d) 7(e) 11 2. Ifis an integer, andis a positive integer, which of the following must also be a positive integer?(a) (b) (c) (d) (e)

3. If , which of the following must be true?I.II.III.(a) I only(b) II only(c) I and II only(d) II and III only(e) I, II, and III4. The sum of 4 distinct integers is 29. If the greatest integer is less than 10, what is the least of the four?(a) 0(b) 3(c) 5(d) 6(e) 7

5. In the three-digit integer, in whichX, Y, and Zeach represent a different integer. Ifis even, how many different integers can it represent?(a) 2(b) 5(c) 8(d) 10(e) 156. Ifris even andtis odd, which of the following is odd?(a) rt (b) 5rt(c) (d) 5r+ 6t(e) 6r+ 5t

7. Provided k is an integer. What is always going to be divisible by?(a) 4(b) 5(c) 6(d) 7(e) 88. The positive integeris not divisible by. Provided that the remainder whenis divided byand the remainder whenis divided byare each equal to. What is? (A)1 (B) 2 (C) 4 (D)6 (E) It cannot be determined by the information above